This invention relates to prosthetic heart valves. More particularly, the invention relates to prosthetic heart valves that can be collapsed to a relatively small circumferential size for delivery into a patient's body with reduced invasiveness to the patient, and which can then be re-expanded to operating size at the intended implant site in the patient. Still more particularly, the invention relates to methods and apparatus for delivering a valve of the type described above into a patient and re-expanding the valve at the implant site. Another possible aspect of the invention relates to methods and apparatus for repositioning the valve in the patient and/or for retrieving the valve from the patient if desired.